The bent leg in math

instagram viewer

The angled leg can be a (application-oriented) task from geometry - but also a way to better remember the number 4 in mathematics.

A bit of sportiness is part of this task.

What you need:

Cosine law (alternatively Pythagoras, sine)
Yardstick
calculator
some sportiness

Note: In this article, the so-called. "angled leg" cannot be explained as a donkey bridge, to memorize number 4 for the purposes of representation. Brace your foot at knee height so that the thigh of the standing leg and the thigh and lower leg of the bent leg form a triangle.

The bent leg as a math problem

This mathematics task starts with a self-experiment, which requires some athletic commitment. You have to stand on your standing leg and bend the other leg. Brace your foot at knee height so that the thigh of the standing leg and the thigh and lower leg of the bent leg form a triangle.
Take the tape measure and measure the lengths of the sides of the triangle. The geometric task is now to calculate the angles in this leg triangle. In general, of course, it will not be a right triangle, but it will be an isosceles one, as the lengths of the two thighs should be the same.
instagram viewer

Leg triangle - a calculated example

For the calculation of the angle when the leg is bent, the mathematics two basic options:

In the isosceles leg triangle, you can either calculate the height with Pythagoras and then calculate the angles with the help of the trigonometric Functions Sine, cosine resp. Calculate the tangent.

Calculating angles on a triangle - explained step by step

Don't panic about math problems! With a good sketch and the right formulas ...

You can use that for general Triangles Apply the applicable cosine law and first calculate an angle in the leg triangle. The other angles result - more simply - from the sum of the angles in the triangle
In the following, the base side (lower leg with foot height) c = 45 cm and for the two equally long sides (upper thigh) a = b = 38 cm the method with the cosine law is used.
The following applies: c² = a² + b² - 2ab cos (γ). Let γ be the angle between the two sides a and b, i.e. at the tip of the triangle. Reshape: cos (y) = [a² + b² - c²] / 2ab. Substitute in the given quantities and you get cos (γ) = [2 _* 38²- 45²]/2 _* 38² = [2888 - 2025]/2888 = 0,3. Use the to calculate for this cosine value calculator (INV COS) the angle γ = 72.54 °.
You can now calculate the two base angles from the sum of the angles, which in the triangle is 180 ° to 53.73 ° each.